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katovenus [111]
3 years ago
13

Use the elimination method to solve the system of equations.

Mathematics
1 answer:
lora16 [44]3 years ago
4 0
5x + 2y = 7
-5x + 4y = 5

You can immediately eliminate the x-terms and subtract:

  2y = 7
  4y = 5
-_____
-2y = 2
   y = -1

Substitute back to find x:

-5x + 4y = 5
5x + 4(-1) = 5
5x - 4 = 5
5x = 9
x = 1.8

Finally, substitute back to check your work:

5x + 2y = 7  =>  5(1.8) + 2(-1) = 7  =>  9 - 2 = 7  <--True
-5x + 4y = 5  =>  -5(1.8) + 4(-1) = 5  =>  -9 - 4 = 5  <--False

Answer:
There is no solution.
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Two number cubes are rolled for two separate events: 
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(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5)

(5,1) (5,2) (5,3) (5,4)

(6,1) (6,2) (6,3)

As can be clearly seen the Sample Space for the event A has 30 elements in it.

Now, it is given in the question that the event A has already occurred and we need to find the probability of the event B occurring <u><em>given that the event A has already occurred.</em></u>

Now, as we can see, from the sample space, only 11 events out of the 30 are the events of interest to us. This is shown in bold below:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5)

(5,1) (5,2) (5,3) (5,4)

(6,1) (6,2) (6,3)

Thus, the probability that the event B occurs given that the event A has already occurred is:

P(B|A)=\frac{11}{30}\approx0.367

In percentage the required probability is 36.7% approximately.

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Step-by-step explanation:


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